1. For the following exercise, complete the following by using the data sets below that provides the ages of the first seven presidents:
a. Find the mean, median, and range for each of the two data sets.
b. Find the standard deviation using the range rule of thumb for each of the data sets. Please show your work. (Please see Chapter 4, Section 4.3, page 173 of the text).
c. Compare the two sets and describe what you discover.
The following data sets shows the ages of the first seven presidents (President Washington through President Jackson) and the seven most recent presidents including President Obama. Age is given at time of inauguration.
First 7: 57 61 57 57 58 57 61
Second 7: 61 52 69 64 46 54 47
Mean = Σx/n
Median: arrange score in order of value. Middle most score = median = 50 percentile. If two scores in middle, get mean of those two.
Mode = most frequently observed score
Range = highest score - lowest.
I don't know what your "rule of thumb" is.
You can do the calculations.
To answer the question, let's break it down into steps:
a. Find the mean, median, and range for each of the two data sets.
1. Mean:
To find the mean (average) of a set of numbers, we add up all the numbers in the set and then divide the sum by the total number of values in the set.
For the first data set (First 7):
57 + 61 + 57 + 57 + 58 + 57 + 61 = 408
Mean = 408 / 7 = 58.29 (rounded to two decimal places)
For the second data set (Second 7):
61 + 52 + 69 + 64 + 46 + 54 + 47 = 393
Mean = 393 / 7 = 56.14 (rounded to two decimal places)
2. Median:
To find the median of a set of numbers, we arrange the numbers in ascending order and find the middle value. If there is an even number of values, we take the average of the middle two values.
For the first data set (First 7):
57, 57, 57, 58, 61, 61
Median = 57
For the second data set (Second 7):
46, 47, 52, 54, 61, 64, 69
Median = 54
3. Range:
To find the range of a set of numbers, we subtract the smallest value from the largest value.
For the first data set (First 7):
Range = 61 - 57 = 4
For the second data set (Second 7):
Range = 69 - 46 = 23
b. Find the standard deviation using the range rule of thumb for each of the data sets.
The range rule of thumb states that the standard deviation can be estimated by taking the range and dividing it by 4.
For the first data set (First 7):
Standard deviation = Range / 4 = 4 / 4 = 1
For the second data set (Second 7):
Standard deviation = Range / 4 = 23 / 4 = 5.75 (rounded to two decimal places)
c. Compare the two sets and describe what you discover.
In comparing the two sets, we can observe the following:
- The mean age for the first data set is 58.29, while the mean age for the second data set is 56.14. This suggests that, on average, the first seven presidents were slightly older at the time of inauguration compared to the seven most recent presidents.
- The median age for the first data set is 57, while the median age for the second data set is 54. This indicates that the middle value in the first data set is slightly higher than in the second data set.
- The range for the first data set is 4, indicating a relatively narrow spread of ages. In contrast, the range for the second data set is 23, suggesting a wider range of ages.
- The standard deviation for the first data set is 1, which indicates less variability in ages. The standard deviation for the second data set is 5.75, indicating more variability or dispersion in ages.
Overall, the comparison reveals some differences in the ages of the first seven presidents versus the seven most recent presidents, both in terms of central tendency (mean, median) and dispersion (range, standard deviation).